A difference-integral representation of Koornwinder polynomials

摘要

We construct new families of (q-) difference and (contour) integral operatorshaving nice actions on Koornwinder's multivariate orthogonal polynomials. Wefurther show that the Koornwinder polynomials can be constructed by suitablesequences of these operators applied to the constant polynomial 1, giving thedifference-integral representation of the title. Macdonald's conjectures (asproved by van Diejen and Sahi) for the principal specialization and norm followimmediately, as does a Cauchy-type identity of Mimachi.